Searching for periodic orbits of the spatial elliptic restricted three-body problem by double averaging

Physica D: Nonlinear Phenomena

Volumn 213, Issue 1, 2006, Pages 15-24

  Palacián, Jesús F ^a   Yanguas, Patricia ^a   Fernández, Silvia ^b   Nicotra, Mariano A ^b  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

^b UNIVERSIDAD NACIONAL DE CÓRDOBA   (Argentina)

Author keywords

Averaging; Celestial mechanics; Invariant manifolds; Periodic orbits; Relative equilibria; Spatial elliptic restricted three body problem; Stability

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HAMILTONIANS; LYAPUNOV METHODS; ORBITS; PROBLEM SOLVING; STABILITY;

AVEERAGING; CELESTIAL MECHANICS; PERIODIC ORBITS; RELATIVE EQUILIBRIA; SPATIAL ELLIPTICAL RESTRICTED THREE-BODY PROBLEM;

ASTROPHYSICS;

EID: 29144454614     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.10.009     Document Type: Article

References (20)

1. S.A. Astakhov, A.D. Burbanks, S. Wiggins, and D. Farrelly Chaos-assisted capture of irregular moons Nature 423 2003 264 267
2. S.A. Astakhov, and D. Farrelly Capture and escape in the elliptic three-body problem Mon. Not. R. Astron. Soc. 354 2004 971 979
3. D. Brouwer, and G.M. Clemence Methods of Celestial Mechanics 1961 Academic Press New York, London
4. J.M. Cors, C. Pinyol, and J. Soler Periodic solutions in the spatial elliptic restricted three-body problem Physica D 154 2001 195 206
5. J.M. Cors, C. Pinyol, and J. Soler Analytic continuation in the case of non-regular dependency on a small parameter with an application to celestial mechanics J. Differential Equations 219 2005 1 19
6. A. Deprit Canonical transformations depending on a small parameter Celestial Mech. 1 1969 12 30
7. A. Deprit The elimination of the parallax in satellite theory Celestial Mech. 24 1981 111 153
8. A. Deprit Delaunay normalisations Celestial Mech. 26 1982 9 21
9. S. Fernández, D. Giuliodori, and M.A. Nicotra Extra-solar massive planets with small semi-major axes? Monogr. Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza 25 2004 115 120
10. J. Henrard Virtual singularities in the artificial satellite theory Celestial Mech. 10 1974 437 449
11. C. Howison, and K.R. Meyer Doubly-symmetric periodic solutions of the spatial restricted three-body problem J. Differential Equations 163 2000 174 197
12. M. Iñarrea, V. Lanchares, J.F. Palacián, A.I. Pascual, J.P. Salas, and P. Yanguas The Keplerian regime of charged particles in planetary magnetospheres Physica D 197 2004 242 268
13. Z. Makó, and F. Szenkovits Capture in the circular and elliptic restricted three-body problem Celestial Mech. Dynam. Astronom. 90 2004 51 58
14. K.R. Meyer Periodic Solutions on the N-Body Problem Lecture Notes in Mathematics vol. 1719 1999 Springer-Verlag Berlin
15. K.R. Meyer, and G.R. Hall Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Applied Mathematical Sciences vol. 90 1992 Springer-Verlag New York
16. J.F. Palacián Invariant manifolds of an autonomous ordinary differential equation from its generalised normal forms Chaos 13 2003 1188 1204
17. J.F. Palacián, and P. Yanguas Invariant manifolds of spatial restricted three-body problems: The lunar case J. Delgado E.A. Lacomba J. Llibre E. Pérez-Chavela New Advances in Celestial Mechanics and Hamiltonian Systems 2004 Kluwer Academic/Plenum Publishers Dordrecht 199 221
18. V. Szebehely Theory of Orbits 1967 Academic Press New York
19. F. Verhulst Nonlinear Differential Equations and Dynamical Systems 1996 Springer-Verlag Berlin
20. P. Yanguas Perturbations of the isochrone model Nonlinearity 14 2001 1 34